It is commonly said that nucleons are made of three quarks, which is true to a point. It is logical to think that each quark has one third the mass of the nucleon, but that's not actually true. The mass of the three quarks in the nucleons make up only about one to two percent of the mass of the nucleons. What makes up the other 98 percent?The Higgs only comes in the explanation for the mass of the quarks themselves, which obviously is only 2% of the mass of a nucleon.
This is where things get cool. First, you need to know that a nucleon is not a static object with three ingredients. A nucleon consists of three very light quarks held together by the strong nuclear force. Those three quarks are moving at high velocities inside the nucleon. To picture this, imagine three ping pong balls in a lottery machine. Those ping pong balls aren't the most important thing; rather, you should focus on what's forcing them into motion. Think of nucleons as three quark flecks, tossed furiously inside a little subatomic tornado. The tornado is far more important than the tiny flecks.
Isn't it interesting that the "god particle" plays such an insignificant role in this case?